Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2

@article{Schiffmann2012CherednikAW,
  title={Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2},
  author={Olivier Schiffmann and Eric Vasserot},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2012},
  volume={118},
  pages={213-342}
}
We construct a representation of the affine W-algebra of ${\mathfrak{g}}{\mathfrak{l}}_{r}$ on the equivariant homology space of the moduli space of Ur-instantons, and we identify the corresponding module. As a corollary, we give a proof of a version of the AGT conjecture concerning pure N=2 gauge theory for the group SU(r).Our approach uses a deformation of the universal enveloping algebra of W1+∞, which acts on the above homology space and which specializes to $W({\mathfrak{g}}{\mathfrak{l}}_… 

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